1 0( degrees ) | N (rpm ) | 37 NAME : Jenelle . Ramrekna 40 1. A simple pendulum of length / and mass m oscillates in the vertical plane, as shown in the figure below: 30 where g is 9.81 m/s and Of) is the angular displacement of the swinging mass. If / = 0.1 meters and m = 0.5 kg, and O(1) = $ sin (it + 7) rad. substitute the values for g and / and complete the following parts. (a) Write down the amplitude, frequency (in Hz), period (in seconds), phase angle (in degrees). and time shift (in seconds) of (t). (5 points) + 17 (b) Plot one cycle of the position ((t) and indicate the earliest time after 1 =0 when the position is zero. (5 points) (c) Suppose the attachment point of the pendulum is able to rotate with the intent to tune the behavior of oscillation Or(t). The total angular response is then given by o(t) = Or(t) - O(t). If the tuning Or(t) = - sin(at). write off) in the form oft) - Mcos ( it + a). in other words find M and a. (10 points) Total Points: 20 2. A missile guidance system tracks two types of cruise missiles fired from two separate locations 3240 miles apart. The missiles are aimed and traveling toward the same target at different velocities. If missile 1 travels 100 mph faster than missile 2 and they both reach the target in 4 hours the following system of equations can be used to determine the exact velocities of each missile represented by my and me. Am1 + 4m12 = 3240 m! = 100 + 12 a) Find my and m2 using the substitution method. (5 points) b) Write the system of equations in the matrix form AM = B, where M = m, . (5 points) c) Find my and m2 using Cramer's Rule. Show all steps. (5 points) d) Find my and my using the matrix algebra method. Perform all matrix computations by hand, and show all steps (no calculator). (5 points) Total Points: 20